Estimation of forest structure metrics relevant to hydrologic modelling using coordinate transformation of airborne laser scanning data

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www.hydrol-earth-syst-sci.net/16/3749/2012/ doi:10.5194/hess-16-3749-2012

© Author(s) 2012. CC Attribution 3.0 License.

Earth System

Sciences

Estimation of forest structure metrics relevant to hydrologic

modelling using coordinate transformation of airborne laser

scanning data

A. Varhola1, G. W. Frazer2, P. Teti3, and N. C. Coops1

1Department of Forest Resources Management, University of British Columbia, 2231-2424 Main Mall, Vancouver, BC,

V6T 1Z4, Canada

2Department of Geography, University of Victoria, 3800 Finnerty Road, Victoria, BC, V8P 5C2, Canada 3BC Ministry of Forests, Lands, and Natural Resource Operations, 200-640 Borland Street, Williams Lake, BC,

V2G 4T1, Canada

Correspondence to: A. Varhola (avarhola@interchange.ubc.ca)

Received: 3 April 2012 – Published in Hydrol. Earth Syst. Sci. Discuss.: 25 April 2012 Revised: 6 September 2012 – Accepted: 19 September 2012 – Published: 23 October 2012

Abstract. An accurate characterisation of the complex and

heterogeneous forest architecture is necessary to parame-terise physically-based hydrologic models that simulate pre-cipitation interception, energy fluxes and water dynamics. While hemispherical photography has become a popular method to obtain a number of forest canopy structure met-rics relevant to these processes, image acquisition is field-intensive and, therefore, difficult to apply across the land-scape. In contrast, airborne laser scanning (ALS) is a remote-sensing technique increasingly used to acquire detailed in-formation on the spatial structure of forest canopies over large, continuous areas. This study presents a novel method-ology to calibrate ALS data with in situ optical hemispher-ical camera images to obtain traditional forest structure and solar radiation metrics. The approach minimises geometrical differences between these two techniques by transforming the Cartesian coordinates of ALS data to generate synthetic images with a polar projection directly comparable to opti-cal photography. We demonstrate how these new coordinate-transformed ALS metrics, along with additional standard ALS variables, can be used as predictors in multiple linear regression approaches to estimate forest structure and solar radiation indices at any individual location within the extent of an ALS transect. We expect this approach to substantially reduce fieldwork costs, broaden sampling design possibili-ties, and improve the spatial representation of forest structure metrics directly relevant to parameterising fully-distributed hydrologic models.

1 Introduction

Forested environments create unique microclimatic condi-tions that modulate a wide array of biophysical processes tightly linked to components of the hydrologic cycle. Struc-tural and physiological characteristics of forests and their relationship to evapotranspiration, interception, soil mois-ture and energy fluxes have, therefore, been intensively stud-ied to develop physically-based models capable of simulat-ing water dynamics in diverse hydroclimate regimes (e.g., Wigmosta et al., 1994; Pomeroy et al., 2007; Kura´s et al., 2012). In snow-dominated regions, forests generally reduce the amount of snow present on the ground prior to the on-set of spring due to snowfall interception and sublimation in the canopies. The attenuation of solar radiation as it passes through forest structural elements is also of particular impor-tance as it controls the rate and timing of snow melt, and hence strongly determines flooding risk levels and seasonal water availability (Varhola et al., 2010a).

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elements (i.e., foliage, branches, boles and gap space) (Hardy et al., 2004). Variations of these factors can create an un-limited array of micro-environments within a forest, each with a distinctive gap distribution that ultimately determines how much of the falling snow and incoming radiation ac-tually reaches the ground (Essery et al., 2007; Hardy et al., 2004). Characterising sub-canopy snow dynamics and radia-tion regimes within a specific spatial unit thus requires quan-tification of this structural complexity into numerical param-eters readily available as inputs for hydrologic models.

Three of the metrics most commonly used to describe for-est structure and its relationship to hydrologic processes are leaf area index (LAI), gap fraction (GF) and sky-view factor (SVF). Although LAI has several definitions (Br´eda, 2003), it is generally described as the ratio of one-half of the total leaf area per unit of ground surface area (Chen et al., 1997). De-spite known difficulties with the accurate estimation of LAI, one of its versions known as effective LAI or plant area in-dex (PAI) has become a key input parameter in physically-based hydrologic models because it directly affects rain and snow interception, wind speed reduction and radiation atten-uation in forested environments (Ellis et al., 2010). GF is the fraction of view that is unobstructed by canopy elements in any particular angular direction (Welles and Cohen, 1996), equivalent to the probability of a light beam passing through the forest to reach a point near the ground (Danson et al., 2007). SVF, used to model absorption of longwave radiation by snow (Wigmosta et al., 2002), is usually defined in hy-drologic models as the fraction of celestial (sky) hemisphere visible from a point near the forest floor (Sicart et al., 2004) and is calculated as a cosine-weighted 180◦integration of GF (Frazer et al., 1999).

Several methods have been developed to directly or directly estimate LAI, GF, and SVF in the field. One in-strument frequently used is the LI-COR® LAI-2000 Plant Canopy Analyser (LAI-2000), which can provide LAI and GF by simultaneously comparing incoming diffuse radiation above and below the canopy (Welles and Norman, 1991). Hemispherical photography (HP) is another popular alterna-tive that uses skyward-looking images taken from beneath the forest to estimate various attributes of canopy structure and to model light penetration over periods of time (i.e., growing season). Both the LAI-2000 and HP are based on a hemispherical projection geometry usually comprising a wide field of view (AOV) (∼180◦for HP and 148◦for LAI-2000), which is fundamental to provide multi-angular esti-mates of GF and, in HP, to account for local solar paths and the angular variation in diffuse sky brightness. Advan-tages of HP over the LAI-2000 are that HP does not require above-canopy measurements of diffuse sky radiation to com-pute GFs and it provides a permanent image of the forest that can be processed with software tools to automatically ob-tain a variety of structural and site-specific radiation parame-ters (e.g., Gap Light Analyser (GLA) (Frazer et al., 1999) or

Hemiview; Rich et al., 1999). Although HP is not free of bias in the presence of heterogeneous lighting conditions and is subject to certain subjectivity when manually binarising the images to separate canopy and sky pixels, it has been vali-dated as a tool to accurately model radiation regimes beneath forest canopies, provided that a few basic local parameters are known (Coops et al., 2004). Hardy et al. (2004), for ex-ample, compared above- and below-canopy incoming global solar radiation measurements from pyranometers with radia-tion transmission estimates obtained from HP, and concluded that both agreed well enough to be interchangeably used in snow models.

One disadvantage of HP, however, is that image acquisi-tion and processing are time-consuming and, therefore, can-not be easily applied to vast, remote areas (Essery et al., 2007). Light Detection And Ranging (LiDAR), on the other hand, is a remote-sensing technology capable of providing three-dimensional representations of canopy structure over large, continuous regions. LiDAR sensors actively emit laser pulses and record the distance between sensor and target, providing point cloud-type representations of the scanned objects. LiDAR systems are generally classified as either Ter-restrial Laser Scanning (TLS) or Airborne Laser Scanning (ALS) according to platform, or as discrete or full-waveform according to the type of digitisation filter (Lim et al., 2003). Discrete ALS sensors mounted on helicopters or airplanes at low flying altitudes (500–1000 m) are currently the most widely used LiDAR systems in forestry (Lee et al., 2009) due to their extensive spatial coverage and sampling densities of one to several laser returns per m2(Wulder et al., 2008).

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geometries associated with HP (upward-looking, angular) versus ALS (downward-looking, near-vertical) sensors make it difficult to establish an exact match between the two tech-niques.

The objective of this article is to develop a methodology to obtain HP-equivalent forest canopy GF, LAI, SVF and solar radiation transmission metrics at any location within a discrete ALS cloud of points. Our approach transforms the Cartesian coordinates of the ALS return cloud into a polar co-ordinate system to produce synthetic, upward-looking hemi-spherical images suitable for processing with specialised software (GLA). Metrics obtained from these images are then calibrated directly with real optical HP counterparts col-lected within a network of ground-reference sites. This novel approach has the following advantages compared to previ-ous studies that have attempted to link ALS and HP met-rics: (1) it is based on the same geometrical projection and, therefore, minimises calibration errors; (2) it takes advantage of the entire functionality of GLA or Hemiview, including the calculation of forest structure parameters and a variety of light indices for user-defined requirements; (3) it is less restricted to any particular spatial resolution associated with ALS cylinder size (Zhao and Popescu, 2009); (4) it does not require direct radiation measurements for validation due to the proven ability of HP to predict radiation regimes (Hardy et al., 2004); (5) it is based on a paired one-on-one com-parison of hemispherical images rather than plot averages, allowing a more detailed exploration of the ideal physical representation of canopies by ALS and the direct input of point-level forest structure metrics into hydrological mod-els to analyse relevant processes at the finest possible scale (e.g., Pomeroy et al., 2007); and, finally, (6) it only requires raw ALS data and HP without relying on manual ground measurements, complementary spectral remote sensing tools or sophisticated tree-reconstruction or stem mapping tech-niques (e.g., Roberts et al., 2005).

The analyses of this study are focused on obtaining the for-est structure metrics that are currently used by most hydro-logic models at any point within an ALS point cloud. The di-rect input of these remotely sensed variables into the models is not tested because the main benefit of this methodology is the better characterisation of canopy structure in space rather than the simulation of hydrologic processes at the point level, which can be achieved with traditional optical HP. Future work will take advantage of the opportunity to generate thou-sands of synthetic hemispherical images derived from ALS to assess the spatial distribution of forest structure metrics relevant to hydrologic modelling at the watershed level, and later fulfill the ultimate goal of allocating fully distributed, spatially explicit versions of these metrics to the models.

2 Methods

2.1 Study area

The study took place in central British Columbia (BC), Canada, near the cities of Quesnel and Vanderhoof (Fig. 1). For a decade, this area has been affected by an outbreak of mountain pine beetle (MPB) (Dendroctonus ponderosae) that significantly changed the landscape by defoliating and killing large continuous forests of lodgepole pine (Pinus con-torta), the dominant species. The Interior Plateau of BC is characterised by cold, dry winters with snow cover for up to seven months every year; snow melt constitutes a main source of water during spring and is also associated with an-nual peak streamflow (Bewley et al., 2010). Since the phys-ical processes that govern snow accumulation and ablation are highly sensitive to changes in forest cover, the impacts of forest disturbance on hydrologic regimes has recently been under intensive research in BC (Bewley et al., 2010; Boon, 2009; Coops et al., 2009; Teti, 2008, 2009; Uunila et al., 2006; Varhola et al., 2010b).

Seven forested plots established by Teti (2008) provided the model calibration data for this study, and are described in detail in Table 1. The first four plots are located in the Baker Creek watershed, near Quesnel, while three are southwest of Vanderhoof. All are characterised by their low-gradient, rel-atively flat terrain and each consists of 36 sampling points separated by 10 m to create a squared 50×50 m grid, as shown on Fig. 1. The plots are representative of the main stand types and their relative predominance in the area at the time of their installation, namely: mature stands (height >15 m) where most of the trees have been severely defoli-ated by MPB (BOD1, BOD3, VOD1 and VOD2); interme-diate (height∼10 m) stands affected by MPB, but with their trees still holding dehydrated, red foliage (BRC2); and young healthy-looking stands (height ∼3 m) (BRC1). An addi-tional plot was located in a dense stand resulting from post-fire regeneration (VYN), with high stem densities and 25 % mortality caused by within-stand competition and ice/snow-related breakage rather than MPB. More information about these plots and the methodology for capturing inventory met-rics and MPB defoliation are available on Teti (2008). Eleven additional plots of a different size and configuration, which included additional stand types such as healthy spruce, were used to validate our methodology at the plot-level.

2.2 Data acquisition for modelling

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Table 1. Stand locations and physical characteristics as of 2008.

General information Ground inventory metrics Foliage appearance (%)b

Plot Stand Latitude Longitude Elevation Stem density DBH Basal area Mean Max. Green Red Grey

codesa description (age) (◦) (◦) (m) (n ha−1) (cm) (m2ha−1) height (m) height (m)

BOD1 Mature heavily 52.676 −123.016 1218 1800 18.5 55.4 18.2 28.9 0 19 77

defoliated stand (216)

BOD3 Mature defoliated 52.638 −122.993 1222 550 25.5 28.7 17.3 26.2 8 14 77

stand (211)

BRC1 Small healthy 52.670 −123.017 1231 1312 5.4 1.1 3.9 5.6 100 0 0

regeneration (10)

BRC2 Medium red-attack 52.672 −123.017 1229 1025 13.5 15.0 10.1 13.5 48 52 0

stand (26)

VOD1 Mature defoliated 53.720 −124.949 902 1387 18.0 19.0 9.0 17.3 22 0 78

stand (135)

VOD2 Mature heavily 53.717 −124.955 836 1687 21.6 55.6 13.2 20.8 5 5 90

defoliated stand (135)

VYN Dense natural 53.719 −124.953 900 7648 8.0 34.0 9.7 14.3 75 0 25

post-fire stand (75)

aFollowing codes by Teti (2008); first letter in code corresponds to the study area.bDefoliation percentage calculated as proportion of basal area falling into each health

category, which are described by Varhola et al. (2010b).

Fig. 1. Study area location within British Columbia (left) including ALS transects (black straight lines in the close-up) and ground plot locations in the Vanderhoof (top left corner ellipse) and Baker Creek (bottom right corner circle) areas; the 2500 m2square ground plots (right) are constituted by 36 individual stakes (spaced 10 m) labelled as letter and number combinations (A1 to F6) (Teti, 2008).

2001), these ideal conditions are rarely present in central BC. To prevent sunlight from directly hitting the lens, Teti (2008) used a small shading paddle which was later eliminated from the images by careful retouching. Although the sampling points were registered by a GPS with differential correction, the exact location of the optical camera when acquiring the HP still contained some error and thus the maximum esti-mated deviation between each point and the actual corre-sponding camera position was approximately 1.5 m.

ALS data were acquired in February 2008 by Terra Re-mote Sensing (Sidney, BC) with a TRSI Mark II discrete re-turn sensor mounted on a Bell 206 Jet Ranger helicopter at a flying altitude of∼800 m above ground level. The sensor’s wavelength was 1064 nm with a pulse repetition frequency of 50 kHz, maximum off-nadir scan angle of 15◦, and a fixed beam divergence angle of 0.5 mrad. A 200 km×400 m ALS transect was acquired over the ground plots in four sepa-rate sections, as shown on Fig. 1, with a resulting average foot-print size of 0.35 m and an average effective density of 4.8 returns m−2. To estimate plot center elevations, a ground-level digital elevation model (DEM) with 5 m pixels (25 m2)

was created by applying the ground filter algorithm used in FUSION® software (McGaughey, 2010) to the ALS data as proposed by Kraus and Pfeifer (1998).

A selection of basic ALS metrics was obtained for each 50×50 m plot to explore the overall variability of forest structure and data configuration (Table 2). The total num-ber of ALS returns per plot was separated into sub-canopy (below 0.5 m) and canopy (above 0.5 m) classes. ALS re-turn density was calculated by dividing the total number of laser returns by plot area (2500 m2), while ALS metadata provided mean absolute scan angle directly. Vertical GF was calculated for each plot as the ratio of sub-canopy returns (>0.5 m) to total ALS returns. A mean canopy height proxy was the average height above ground of all canopy returns (different from mean tree height). In all cases, no distinction was made between first and other return types.

2.3 Synthetic ALS hemispherical image generation

ALS data was extracted for 75 m radius cylinders centered at each of the sampling points, a size chosen to ensure that enough ALS returns were included closer to the horizon to mimic the infinite viewing distance of optical HP, yet small enough so that the entire cylinders fitted into the 400 m-wide data transect. Only the three northernmost rows of plot VOD1 were excluded as they were too close to the ALS boundary, thus reducing the sample to a total of 234 cylders. All the ALS returns (first, intermediate, last) were in-cluded in the cylinders to maximise density as proposed by Todd et al. (2003) and Lee et al. (2009).

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Table 2. ALS simple metric summary for each major plot.

Plot Stand Total Ground Canopy Return Mean Vertical Maximum Mean canopy

codes description (age) ALS ALS ALS density absolute gap return return height returns returns returns (n m−2) scan angle (◦)∗ fraction height (m) (m)∗

BOD1 Mature heavily 13 521 10 042 3479 5.4 0.6 (118) 0.74 25.7 12.7 (55)

defoliated stand (216)

BOD3 Mature defoliated 21 209 16 070 5139 8.5 7.7 (49) 0.76 23.8 12.3 (51)

stand (211)

BRC1 Small healthy 18 273 15 275 2998 7.3 5.0 (32) 0.84 4.2 1.3 (52)

regeneration (10)

BRC2 Medium red-attack 19 232 10 393 8839 7.7 4.2 (48) 0.54 11.6 5.5 (53)

stand (26)

VOD1 Mature defoliated 17 095 12 899 4196 6.8 13.7 (9) 0.75 20.5 7.0 (68)

stand (135)

VOD2 Mature heavily 17 014 13 611 3403 6.8 3.9 (46) 0.80 20.4 11.9 (42)

defoliated stand (135)

VYN Dense natural 19 699 9279 10 420 7.9 6.1 (27) 0.47 12.8 6.0 (46)

post-fire stand (75)

Coefficients of variation (%) from individual returns in parentheses.

of view were eliminated from the 75 m cylinders to increase data processing efficiency. The XYZ positions of all the re-maining returns were transformed with simple trigonometry to polar coordinates composed of angles of azimuth (◦) and zenith (◦), and distance (m) with respect to each HP reference position. Finally, angles of azimuth were flipped in an east – west direction to reflect an upward-looking field of view as in HP.

The fine-scale representation of physical vegetation struc-ture by individual ALS returns is not well understood, and several assumptions are therefore required to convert laser points into geometrically simplified, 3-D plant structures. We undertook a sensitivity analysis on a subsample of calibration plots to explore the impact of three main parameter settings related to projected canopy element size and shape: (1) pro-jecting returns with a fixed or variable size (inversely propor-tional to distance), or a combination of the two; (2) minimum ALS return circle size for fixed projections; and (3) ALS re-turn sphere size for variable projections. More details about these parameters and their implications are clarified below as the methodology for generating the synthetic images is ex-plained. The optimal parameter settings were chosen by eval-uating scatter plots and correlation coefficients of observed GFs in real versus synthetic images, while keeping the other parameters constant. Figure 2 shows an example testing three different minimum fixed projected sizes.

Based on the results of the sensitivity analysis, each ALS return was represented as an opaque sphere with a 15 cm diameter centered on the original ALS XYZ return loca-tion. These spheres were projected as black circles on a two-dimensional plane to create one synthetic hemispherical im-age for each sampling cylinder. Calculating the diameter of each projected ALS return first required the selection of an

arbitrary radius to the circular images (r)and a theoretical fo-cal length (f ), both 10 cm. The ratio between the projected (rp) and full-scale ALS return radii (rr) is then assumed

equivalent to the ratio between the focal length (f )and the absolute distance between the return’s centroid and the cam-era position(d):rp/rr=f/d. This is illustrated in Fig. 3a.

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Table 3. Hemispherical photo parameter calibration.

Parameter Definition∗/source of information Baker Creek Vanderhoof

Latitude (◦) Average of study area plots 52.664◦N 53.719◦N

Longitude (◦) Average of study area plots 123.011◦W 124.952◦W

Elevation (m) Average of study area plots 1230 903

Slope/aspect (◦) Average of study area plots 0/0 0/0

Solar time step (min) Time interval for which the sun’s position is measured between sunrise and sunset for the full length of the growing season. GLA default value used.

5 5

Growing season start/end These dates affect the range in the solar declination for the period of interest. In this case, the growing season was approximated to the winter period due to our later interest in snow processes.

1 October/31 May 1 October/31 May

Azimuth/zenith sky regions Discrete areas of the sky hemisphere separated by equal-interval divisions of azimuth and zenith.

16/18 16/18

Data source Method for deriving growing season above-canopy solar radiation data.

Modelled Modelled

Solar constant (W m−2) Total radiant flux of the sun on a perpendicular surface located outside the Earth’s atmosphere at a mean distance of one astronomical unit. GLA default value used.

1367 1367

Cloudiness index Site-specific measurement of cloudiness: fraction of extraterrestrial radiation that reaches the ground surface as total solar radiation. Values for both sites calculated as an average fraction of daily GLA-modelled extraterrestrial radiation and radiation measured in a weather station located in the Baker Creek area (Bewley et al., 2010).

0.49 0.49

Spectral fraction Fraction of global solar radiation (0.25 to 25.0 µm) incident on a horizontal surface at the ground that falls within a limited range of the electromagnetic spectrum. Values set to 1.0 to include the entire spectrum.

1.0 1.0

Units Units of measure used to compute the incident radiant flux density data output.

MJ m−2d−1 MJ m−2d−1 Beam fraction Ratio of direct to total spectral radiation incident on a horizontal

surface at the ground over a specified period, which is a function of cloud cover for supra-daily periods. Values calculated from cloudiness index as explained by Frazer et al. (1999).

0.44 0.44

Sky region brightness Method for describing the intensity of the solar disk and diffuse sky. The selected Standard Overcast Sky (SOC) assumes that the zenith is three times as bright as the horizon.

SOC SOC

Clear sky transmission coefficient Factor that describes the regional clarity of the atmosphere with respect to the instantaneous transmission of direct (beam) radiation. Value used recommended for the area by Frazer et al. (1999).

0.6 0.6

All definitions taken from Frazer et al. (1999).

The radial location of ALS returns in the synthetic images followed the same equiangular projection produced by the optical lens system (FC-E8 fisheye converter) used to collect the real HP images (Inoue et al., 2004), where the radial dis-tance from the centre of the image is directly proportional to the zenith angle (Rich et al., 1999). A projection based solely on variable diameters resulted in unrealistic-looking images with distant returns appearing too small to be detected as dark pixels. To avoid this, a minimum base constant return diameter (2.15 mm within a 20 cm diameter image, in this case; Fig. 2) was assigned to all returns in the images so that only those returns close enough to the HP reference to ex-ceed this diameter were projected at variable, larger sizes. Finally, ALS returns closer than 75 cm to the reference were eliminated in accordance with the HP field procedures, which specified a minimum distance between foliage and camera lens for protection purposes and to eliminate the possibility

of having a large proportion of the optical field of view ob-scured by a single foliage unit.

Each synthetic image was generated as a 750×750 pixel bitmap image file (BMP). All 234 files were automatically created in 5 min and 15 s using MATLAB® (1.3 s/image) on a 2.66 GHz, 4.0 GB RAM, 64-bit computer.

2.4 Data processing

2.4.1 HP analysis

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Table 4. Variable acronyms and description.

Variable Units Code Definitiona GLA output Modelling Source

column # role

Optical HP gap fraction – FGFθ Fraction between # of sky and total # of

pixels summed for angles<=θ

10/6

Dependent (YS Optical HP processed

Optical HP total radiation transmittance MJ m−2d−1 FRTθ Absolute amount of total

(di-rect + diffuse) below-canopy radiation summed for angles<=θ

32

orYM) with GLA Optical HP sky-view factor % FSVFθ Percentage of total sky area found in

canopy gaps summed for angles<=θ

20

Optical HP leaf area index m2m−2 FLAIθ Half of total effective leaf area per unit

ground area integrated for angles<=θ.

From appended outputb

ALS gap fraction – LGFθ Same as FGFθ 10/6

Synthetic ALS ALS total radiation transmittance MJ m−2d−1 LRT

θ Same as FRTθ 32 Main hemispherical

ALS sky-view factor % LSVFθ Same as FSVFθ 20 independent images processed

ALS leaf area index m2m−2 LLAIθ Same as FLAIθ From appended (X1) with GLA

outputb

ALS vertical gap fraction – LVGF Ratio of ground/total –

ALS returns

ALS canopy return mean height m LMH Mean ALS return height – Supporting ALS raw data in

above ground independent cylinders with

ALS return density n m−2 LD ALS return spatial density (X

2,X3,X4, radius matchingθ

(including ground returns) X5)

ALS mean scan angle ◦ LSA Mean absolute ALS scan angle

aAll definitions of GLA-derived variables have been taken from Frazer et al. (1999), where they are described with more detail.bFLAI

θand LLAIθare obtained from the

appended output of GLA, where LAI 4 ring corresponds toθ=60◦and LAI 5 ring corresponds toθ=75. For additional information on LAI see Welles and Norman (1991)

and Stenberg et al. (1994).

Table 4 describes the output variables obtained from the GLA analysis for each HP and synthetic image for the 234 sample locations. All of the variables except LAI were numerically integrated across the following zenith angle AOV (θ): 0–30, 0–45, 0–60, 0–75 and 0–90◦. Lower zenith angle limits were included here to allow later explorations of their relation-ships with hydrologic processes, based on previous findings. Teti (2003), for example, concluded that a 0–30◦zenith AOV was most effective at explaining differences in snow storage in the presence of different sized gaps. In addition, sky re-gions including the 0–45◦and 0–60zenith ranges contain most of the solar paths directly responsible for spring melt in our study area. FLAIθ and LLAIθ (defined on Table 4)

automatically integrate LAI for zenith angles of 60 and 75◦ (Welles and Norman, 1991; Stenberg et al., 1994).

In light of intensive discussions and debate about true LAI derivation for decades (Br´eda, 2003), we highlight that this study is only focused on the version of LAI that has been widely used in hydrologic models: that obtained from LAI-2000 or HP, commonly known as effective LAI (eLAI) or plant area index (PAI) (e.g., Pomeroy and Dion, 1996; Bew-ley et al., 2010). It is not our goal to correct for clumping, isolate foliage from stems or formulate hypotheses about the angular distribution of leaves because more nuanced (or sim-ply different) versions of LAI would also require the repa-rameterisation of existing hydrologic models. In this respect, LAI obtained from optical HP is considered as our ground-truth variable.

2.4.2 Standard ALS metrics

The traditional ALS metrics (without coordinate transforma-tion) listed at the bottom of Table 4 were calculated from variable-size cylinders whose diameter hypothetically inter-cepted the canopies at each zenith AOV (θ) based on plot-level maximum tree height (Table 1) (forθ= 90◦, cylinder diameters calculated forθ= 75◦were used). From these point clouds, vertically projected gap fraction (LVGF), mean laser canopy height (LMH), return density (LD) and scan angles (LSA) were estimated for each of the field plot locations (Ta-ble 2). LVGF and LMH are important descriptors of stand structure, while LD and LSA are principally related to ALS sensor configuration and data acquisition conditions, all po-tentially important sources of variation as shown in Table 2. More specifically:

– LVGF represents a downward-looking ALS

ground-to-canopy return penetration ratio known to be well cor-related with upward-looking HP sky/canopy GFs (Sol-berg, 2010);

– LMH is an indicator of stand height and provides

sub-stantial differentiation between stands;

– LD accounts for the varying ALS return density among

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Fig. 2. Effect of projected ALS return size on the relationship be-tween observed and predicted gap fractions. The projected circle size of synthetic image examples (a, b, c) and corresponding rela-tionships (d, e, f) is expressed as the fraction between the diameter of each ALS return and the diameter of the image: 0.0137 (a, d), 0.0176 (b, e), and 0.0215 (c, f).

and must be explicitly accounted for when neighbour-ing or intersectneighbour-ing datasets result in higher numbers of returns (our ALS data was restricted to a single flight line and not subject to changes in density due to over-lap);

– LSA increases from the centre of the flight line (nadir)

towards the swath edge and changes the probabilities of ALS hitting different canopy sections. For example, if scan angles are too large, laser pulses are less likely to penetrate the canopy because of a higher probability of being intercepted, resulting in a different spatial repre-sentation of the forest (Korhonen et al., 2011).

2.5 Regression modelling

GF, LAI, SVF and total direct and diffuse (global) radia-tion transmittance are GLA outputs directly applicable in hy-drologic simulators (e.g., Wigmosta et al., 1994), and were,

Fig. 3. Example of the projection of an ALS spherical return into a 2-D focal plane (a), and azimuthal radial distortion correction at representative zenith angles (b).

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Both simple and multiple linear regression analyses were applied to predict the four HP-derived metrics:

YS(θ )=b0+b1X1(θ ) (1)

YM(θ )=β0+β1X1(θ )+β2X2+β3X3+β4X4+β5X5 (2)

whereθis the maximum zenith AOV for metric aggregation (30, 45, 60, 75 and 90◦);YS andYM can be either FGFθ,

FRTθ, FSVFθ or FLAIθ;X1is the ALS-derived counterpart

ofYS orYM (LGFθ, LRTθ, LSVFθ, or LLAIθ, respectively);

X2corresponds to LVGF,X3is LMH;X4is LD; andX5is

LSA. Please refer to Table 4 for a comprehensive definition of these variables.

Correlations between the dependent variables and each of the independent variables were examined through scatter-plots, and a correlation matrix between all predictor variables (plus FGFθ)was produced to ensure that variables with high

inter-correlations were not added prior to fitting the models. Equations (1) and (2) were fitted using ordinary least-squares regression for each zenith AOV (θ) metric. Also, in order to justify the need and benefit of performing ALS co-ordinate transformations, a simple linear model was fitted to predict HP gap fraction (FGFθ)with the vertical ALS gap

fraction (LVGF) only:

YS(θ )=b0+b1X1 (3)

whereYS(θ )is the same as for Eq. (1) andX1corresponds to

either simple LVGF or the transformation used by Solberg et al. (2006): ln(LVGF−1).

Choosing the best common multiple regression model structure followed a manual backward stepwise approach for variable selection. The intercept and all five predictor vari-ables (Eq. 2) were initially included in the regression to ob-tain a matrix of coefficient p-values that included the entire response variable – zenith AOV model combinations. Model coefficients of the supporting predictor variables (X2. . .X5)

that were significant less than twice in the matrix were re-moved until only those variables consistently showing statis-tical significance across all models were identified. The equa-tions were then validated using the tests described below.

Goodness of fit was evaluated based on the models’ ad-justed coefficients of determination (r2 and R2) and three versions of root mean squared error: absolute (RMSE), leave-one-out cross-validation average derived by iteratively re-fitting the model with all but 1 of 9 randomly generated data groups (RMSES), and normalised by the range of

ob-served values to enable comparisons between different vari-ables (RMSEN). All models were validated by observing the

significance probability (p)of the regression coefficients and by performing Anderson-Darling and Shapiro-Wilk normal-ity tests on the residuals, which confirmed the required nor-mality ifp > α (in all tests,α=0.05). Linearity and vari-ance stability was assessed through visual inspection of pre-dicted vs. observed and prepre-dicted vs. residual scatterplots.

95 % prediction and confidence intervals were calculated and illustrated on the predicted vs. observed figures. For multi-ple regression, the confidence intervals were estimated with a quadratic function relating individual predicted values to their corresponding lower and upper limits as generated by the statistical software (I=c0+c1×P+c2×P2, where

I= upper or lower interval limit, P= predicted value and c0,c1andc2are model coefficients). Variance inflation

fac-tors were also estimated to check for multicollinearity (Field, 2005).

2.6 Plot-level ground-truth model validation

Using the methodologies presented here, new and different grids of synthetic hemispherical images were generated in the same calibration plots and an additional set of 11 plots (other than those in Table 1) as part of a follow-up study. The resulting average GFs were compared with those esti-mated from pre-existing optical HP available in these plots. Although the number and distribution of synthetic and op-tical HP differed substantially within each plot, this com-parison was very useful to validate our methodology with an independent dataset and justify the need for ALS coordi-nate transformation even if plot-level averages were required. This was done by contrasting the relationship between op-tical HP-derived GFs and both a simple ratio of raw ALS ground/canopy returns (calculated as LVGH, but for the ex-tent of individual square plots) and GFs derived from syn-thetic hemispherical images.

3 Results

3.1 Preliminary sensitivity analysis

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3.2 ALS-derived synthetic hemispherical photos

Figure 4 shows examples of ALS return clouds with cor-responding synthetic and actual HP for six common stand structure types found in the study site. In general, there is good visual agreement between the HP and synthetic images across the stands, although the return density (∼

5 returns m−2)of this ALS dataset makes identification of individual trees difficult. In the taller stands (BOD1-C5, BOD3-C4), larger and continuous gaps in the forest canopy are apparent at smaller zenith angles of both the actual and synthetic images. Denser and more homogeneous canopies (BRC2-C1, VYN-B4) show a more even distribution of canopy elements (i.e., ALS returns) across all the zenith an-gles. Markedly different to the other stands is the young re-generation (BRC1-A3), where images are dominated by sky and shorter, clumped vegetation leads to interception of ALS returns much closer to the projection reference.

3.3 Relationships between variables

The correlation matrix between GF as derived from the actual HP (FGFθ)and estimated from the synthetic images (LGFθ)

for the five zenith AOV is shown in Table 5. The relationship between the ALS and HP-derived GFs is significant at all zenith angles and becomes stronger as zenith AOV increases (r=0.75 forθ=30◦andr=0.93 forθ=90◦).

In addition, Table 5 summarizes correlations between the two angular GFs (FGFθand LGFθ)and the ALS simple

met-rics (LVGF, LMH, LD, LSA), which are generally poor. The best correlation occurred between mean LMH and LGFθ,

suggesting that taller stands have a smaller GF across all zenith angles. The correlations between the predictor vari-ables to be input in the multiple regression model (Eq. 2) are generally weak, so redundancy is not likely introduced.

Scatterplots between FGFθ and LGFθ are shown for all

zenith AOV on Fig. 5a–c. Differences in structure across the stands result in distinct population clusters clearly visible in the figures, which prevent fitting a single model to the data.

The relationship between LGFθ and FGFθ shows that,

with the current parameter setup, the synthetic images un-derestimate GF when compared to HP, with the exception of stand BOD3. The young regeneration stand (BRC1) also de-viates from the LGFθ–FGFθgeneral linear pattern and shows

a considerably higher variability.

3.4 Simple linear regression

The simple regression model predicting FGFθfrom ALS

un-transformed data (Eq. 3) was weak across all zenith AOV (r2 ranging from 0.31 to 0.41). Adjusted r2 values in-creased (0.59–0.87) and RMSE dein-creased when the ALS transformed variable (LGFθ)was used; however, nearly all

the simple linear regression models failed residual normal-ity tests. This is illustrated in Fig. 5d–f, where scatterplots

Fig. 4. Representative examples of ALS point clouds (left), ALS synthetic hemispherical images (centre) and real optical hemispher-ical photographs (HP) (right) for each stand; azimuths (◦)are shown on the hemispherical illustrations.

of observed vs. predicted gap fractions indicate that a sin-gle regression line does not account for different populations of stand structures, particularly within the short regeneration stand (BRC1).

3.5 Multiple linear regression

After applying multiple regression to Eq. (2) with all the pre-dictor variables included, LMH proved to be non-significant forθvalues of 30◦and 45◦in all cases and for FLAI60 and

FLAI75, while LSA was consistently non-significant across

all model specifications. The intercept (β0)and LVGF were

not significant in two cases only and were, therefore, main-tained for a second run. After eliminating LMH and LSA from the regression, all of the remaining parameters were statistically significant with no exception. However, models for θ=30◦ did not pass the two residual normality tests, and the FLAI60 model barely passed the Anderson-Darling

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Fig. 5. Relationship between ALS-derived (LGFθ)and HP-derived gap fraction (FGFθ)(a, b, c) and between predicted and observed values

of gap fraction obtained from simple (d, e, f) and multiple (g, h, i) linear regression models across three representative zenith angle AOV (30◦, top; 60◦, centre; and 90◦, bottom); legends in sub-figures (a) and (i) apply to all.

non-normality of residuals in these cases while maintaining our modelling strategy. None of the transformations tested (i.e., inverse, square, square-root, log) solved the problem for FGF30, FRT30 and FSVF30. However, using the square

root of FLAIθ (FLAI0θ.5) allowed the models to pass the

Anderson-Darling test without losing variable significance while improvingR2and RMSE.

Thus, the model that complied with the all the conditions was:

YM(θ )=β0+β1×X1(θ )+β2×X2+β4×X4 (4)

Regression results for Eq. (4) are provided in Table 6, which shows that model behaviour was very similar for all depen-dent variables. Adjusted R2 improves as zenith AOV in-creases due to more pixel aggregation that reduces the prob-ability of canopy returns being assigned to the wrong sky re-gion. RMSEN are very similar for FGFθ, FSVFθ and FRTθ

with the sameθ, while the prediction accuracy of all models

is validated by the consistent similarities between RMSE and RMSES(Kutner et al., 2005). The fitted parameter estimates

ofβ0,β1,β2andβ4shown in Table 6 can be readily used to

predict FGF, FSVF, FRT and FLAI at location within the cur-rent ALS data. All models produced variance inflation factors ranging between 1.3 and 1.7, eliminating multicollinearity concerns (Myers, 1990).

Scatterplots of predicted vs. observed values of FGFθ are

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Fig. 6. Relationship between gap fraction predicted from multiple linear regression (Eq. 4) (YM(θ ))and model residuals (FGFθ−YM(θ ))for

three representative zenith angle AOV.

Table 5. Correlation matrix showing the coefficient of correlation (r)between variables used in multiple regression (gap fraction only, for simplicity); non-significant (p >0.05) values shown in italic.

Zenith FOV (θ ) Variable FGFθ LGFθ LVGF LMH LD LSA

30

FGFθ –

LGFθ 0.75 –

LVGF 0.56 0.42 –

LMH −0.41 −0.72 0.10

LD −0.37 −0.46 −0.57 0.30 –

LSA 0.11 0.010.02 0.17 0.51

45

FGFθ –

LGFθ 0.85 –

LVGF 0.65 0.45 –

LMH −0.50 −0.77 0.09

LD −0.20 −0.25 −0.38 0.03

LSA 0.21 0.11 0.13 0.05 0.45 –

60

FGFθ –

LGFθ 0.89 –

LVGF 0.64 0.48 –

LMH −0.55 −0.77 0.10

LD 0.030.06 −0.27 −0.22 –

LSA 0.24 0.15 0.24 0.01 0.42 –

75

FGFθ –

LGFθ 0.92 –

LVGF 0.62 0.47 –

LMH −0.56 −0.75 0.18 –

LD 0.07 0.00 −0.30 −0.32 –

LSA 0.20 0.13 0.34 0.07 0.17 –

90

FGFθ –

LGFθ 0.93 −

LVGF 0.63 0.50 –

LMH −0.56 −0.73 0.18 –

LD 0.08 0.01 −0.30 −0.32 –

LSA 0.20 0.13 0.34 0.07 0.17 –

Figure 7b indicates that plot-level GF averages from op-tical HP are closely related to averages from new synthetic ALS images, both obtained for all the plots where ALS was available in the study area. The comparison between Fig. 7a and b constitutes strong evidence to justify coordinate trans-formation to accurately predict GF.

4 Discussion

The discussion regarding the methodology presented in this study is centred around the following questions: (1) how do synthetic hemispherical ALS images visually compare to

their real HP counterparts and what are the main sources of error?; (2) how suitable is discrete ALS to represent the fine-scale canopy elements responsible for radiation transmis-sion?; (3) how effective was the proposed modelling strat-egy aiming to predict HP-derived metrics from coordinate-transformed ALS?; (4) what are the perceived benefits of the methodology?; and (5) what lines of action are needed to im-prove and apply this approach in future research?

4.1 ALS synthetic hemispherical images

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Fig. 7. Comparison between the relationship of plot-level average gap fractions obtained from optical HP and (a) vertical gap frac-tion estimated from untransformed ALS, and (b) gap fracfrac-tions from calibrated synthetic hemispherical images.

4.2 Physical representation of canopy elements with ALS

Successful transformation of the ALS point cloud into real-istic synthetic HP images depends on a number of factors. First, the density of laser returns needs to be high enough to capture the basic geometry of individual tree crowns and branches. Second, the size and shape of projected syn-thetic canopy elements (in this case spheres) must be closely related to some basic unit of light-intercepting foliage or branch structure found in real forests. Third, the density and distribution of laser returns must be relatively uniform throughout the entire survey area to avoid bias.

It was shown here that a minimum constant projected size was necessary for all returns to resemble HP; how-ever, inverse-distance-weighted variable projections were still necessary for returns closer to the reference, particularly for the short regeneration stand. ALS returns portrayed as opaque spheres represent a crude approximation of canopy structure as seen by a camera. Real canopy elements are far more complex, but because it is impossible for discrete ALS returns to accurately characterise fine-scale details of

plant canopies, some arbitrariness is inevitable when assign-ing theoretical shapes and sizes to ALS returns. It must be highlighted that our methodology was not designed to repro-duce the scale of detail found in real HP images as possible with higher density TLS (Cˆot´e et al., 2009), but to capture the basic patterns of canopy structure responsible for light interception and penetration that may in turn influence snow accumulation and melt.

The detection of canopy elements by ALS and HP are both dependent on optical properties of the canopy; however, the former technique is based on reflectivity while the latter on opacity. Another disparity between HP and ALS is that the downward, near-nadir view angle of ALS provides a biased vertical profile of forest canopies in which upper elements have a higher probability of being detected, leading to an under-representation of lower branches and stems (Hilker et al., 2010). This may be compensated in synthetic ALS hemi-spherical projections because image saturation increases to-wards the horizon mainly due to the corresponding exponen-tial increase in the number of ALS returns, while in HP it is common to observe tree stems closer to the camera oc-cluding the farther views as the main source of saturation. This will have an effect on the amount of unexplained vari-ance in the regression models, but the strength of model fits (adj.R2=0.8 to 0.92) for FGF, FSVF, FRT, and FLAI sug-gest that any bias in height distribution has little effect on the results. While some of these shortcomings might be min-imised by more sophisticated individual tree-reconstruction routines, volumetric rendering or ray-tracing methods, the corresponding uncertainties here are partly masked and ab-sorbed by the calibration models.

In this study, we made several assumptions about the size and shape of a specific combination of predictors and pa-rameter estimates were chosen so that the empirical relation-ship between canopy metrics derived from synthetic and real HP and their visual similarity was maximised. This method-ology, empirical in nature, is admittedly susceptible to in-teractions between parameters. For instance, a larger mini-mum projected circle size (Fig. 2) might be needed if ALS return density is lower, or the maximum sphere size could be reduced if returns are too close to the reference. Applying this methodology to a wider combination of forest stands and ALS datasets is required to evaluate parameter stability and optimisation.

4.3 Modelling strategy

Regression models using simple vertical gap fractions (LVGF or ln(LVGF−1)) to estimate HP metrics generally had lowr2, high RMSENand produced model residuals that

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Table 6. Multiple linear regression results (refer to Table 4 for RMSE and RMSESunits).

Model Zenith Adjusted RMSE RMSES RMSEN β0 β1 β2 β4 p Anderson- p

Shapiro-variablesa cut (θ ) R2 Darling Wilk

FGFθ/ 30 0.64 0.10 0.10 0.13 −0.15b 0.71c 0.39c 0.01b 0.00 0.00

LGFθ 45 0.82 0.07 0.07 0.10 −0.24c 0.68c 0.44c 0.00c 0.37 0.29

60 0.88 0.06 0.06 0.08 −0.34c 0.63c 0.42c 0.03c 0.16 0.17

75 0.91 0.05 0.05 0.07 −0.38c 0.57c 0.41c 0.03c 0.58 0.89

90 0.92 0.03 0.04 0.06 −0.26c 0.52c 0.28c 0.02c 0.53 0.74

FSVFθ/ 30 0.64 1.28 1.28 0.13 −2.02b 0.71c 5.18c 0.13b 0.00 0.00

LSVFθ 45 0.82 2.00 2.03 0.10 −7.07c 0.68c 12.77c 0.39c 0.40 0.28

60 0.88 2.83 2.86 0.08 −17.2c 0.64c 21.37c 1.36c 0.15 0.19

75 0.91 3.54 3.58 0.07 −28.26c 0.58c 30.99c 2.40c 0.61 0.79

90 0.92 3.67 3.71 0.06 −27.32c 0.53c 30.52c 2.45c 0.60 0.71

FRTθ/ 30 0.65 0.15 0.15 0.13 −0.25b 0.73c 0.59c 0.02b 0.00 0.00

LRTθ 45 0.81 0.27 0.27 0.10 −0.82c 0.68c 1.60c 0.05c 0.51 0.67

60 0.86 0.39 0.39 0.08 −1.92c 0.62c 2.56c 0.17c 0.69 0.96

75 0.89 0.46 0.46 0.08 −3.02c 0.57c 3.55c 0.27c 0.08 0.07

90 0.89 0.47 0.47 0.08 −3.13c 0.55c 3.66c 0.29c 0.10 0.07

FLAIθ/ 60 0.76 0.25 0.25 0.10 2.32c 0.61c −1.53c −0.09c 0.06 0.00

LLAIθ 75 0.76 0.29 0.29 0.11 2.61c 0.59c −1.76c 0.11c 0.01 0.00

FLAI0θ.5/ 60 0.80 0.12 0.12 0.08 1.63c 0.33c −0.82c −0.04c 0.36 0.01

LLAIθ 75 0.81 0.12 0.12 0.09 1.75c 0.30c −0.82c −0.06c 0.08 0.00

aDependent (Y

M)/main independent (X1)variables; supporting variablesX2andX4are common for all models.bSignificant with 0.01<=p <0.05;cSignificant withp <0.01.

Simple linear regression directly estimating HP metrics from their ALS-derived counterparts (X1) was also

unsuccess-ful because it failed to include other key explanatory vari-ables (namely LVGF and LD) and describe the relationships among all stands in one single model, especially due to the deviations shown by BRC1 and BOD3 (Fig. 5). However, the need to perform coordinate transformations of ALS data to better predict HP-derived metrics in individual sampling points was strongly justified (Fig. 7).

Multiple linear regression was suitable to calibrate ALS metrics with HP by accounting for both forest structure and data configuration properties. The models’R2values above 0.80 and RMSENbelow 10 % across all zenith AOV higher

than 45◦ suggest that confident predictions can be made throughout the entire ALS transect. This idea is also sup-ported by the wide structural diversity of stands included in the regression dataset and the successful validation per-formed at plot-level averages in additional stands which rep-resented even more diverse conditions (Fig. 7). Better HP ge-ographical registrations and simultaneous HP/ALS data col-lection plus a detailed outlier analysis are required to fully validate the models forθ=30◦.

A strong component of this study involved the use of a large network of individual ground-reference samples representing a heterogeneous collection of forest structure conditions that appropriately represented both within- and between-stand variability. The latter was particularly impor-tant to understand the relationship between GF derived from

ALS synthetic images and HP across a broad range of GF estimates (e.g., 0.3 to 0.9 forθ=60◦, Fig. 5h). A more com-plete sample of stand structures would have included mature, non-defoliated pine stands; however, this stand type was ab-sent from the study area at the time of data collection. The ac-curacy of predicting HP metrics directly with ALS synthetic counterparts should be independent of stand health status in light of both ALS and HP being able to detect defoliation (Solberg et al., 2006).

The developed models (Eq. 4, Table 6) proved suitable for our range of sampled forest structures and ALS data. Consequently, they need to be tested and validated for dif-ferent stand types (species, densities, heights, health, etc.) and other ALS data acquisitions (e.g., return density, scan angle, footprint size, overlapping transects, return classes, etc.). Of particular interest is the application of this method to full-waveform (FW) LiDAR data, which will be increas-ingly used in the future and provides a more detailed profile of canopy elements and additional radiometric information (Pirotti, 2011). FW LiDAR also has the potential to assist in the improved estimation of the return dimensions by the anal-ysis of target backscatter cross sections (Wagner et al., 2006, 2008). However, given that discrete ALS has been used ex-tensively in many regions, our methodology is not likely to become obsolete in the near future.

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this approach is applied in a different area. This includes re-assessing variable significance and full model validation. It is especially important to account for changes in ALS density caused by systematic overlapping multiple transects, where duplicate sampling might not be properly captured by LD alone. A voxelization of the ALS point cloud might minimise the effect of varying return densities, whereby each volume element (voxel) is coded as one if occupied by one or more ALS returns, or as zero if empty (Cˆot´e et al., 2009).

4.4 Methodological advantages and applicability

There are a number of advantages associated with transform-ing ALS coordinates to generate hemispherical synthetic im-ages. First, geometrical discrepancies between ALS and HP are minimised, allowing a direct comparison of structural and radiation metrics at the individual point level. Second, the methodology is simple because it is based on raw ALS point-cloud data and avoids the need for elaborate canopy models while minimising the number and complexity of geometrical parameters. Third, GLA or other specialised programmes can be used to directly estimate GF, LAI, SVF and local trans-mission of direct, diffuse or total radiation through forest canopies. We have chosen to generate synthetic hemispher-ical images from ALS which are then readily available for processing with GLA because hemispherical photography has become one of the most popular methods to obtain GF and associated forest structure metrics, and its outcomes have been systematically used to parameterise hydrologic models (e.g., Woods et al., 2006; Ellis and Pomeroy, 2007; Ellis et al., 2011). Alternative approaches might produce versions of these metrics that can deviate substantially from those used to develop existing process-based equations, thus requiring their parameters to be revised. Fourth, generating synthetic hemispherical images from ALS introduces unlimited flexi-bility in terms of sample size and experimental design lay-outs: any number of images can be obtained at user-defined spacing options and sub-pixel specific locations. Fifth, single calibration models for each variable proved to be applicable to a wide range of stand types. Finally, variables directly ap-plicable to hydrologic modelling can now be obtained at any point within ALS datasets – significantly reducing fieldwork requirements while improving the parameterisation of vege-tation classes at the landscape-level. The normal distribution of the calibration models’ residuals suggests that our method is unlikely to produce systematically biased estimates of for-est structure variables, which will benefit fully-distributed hydrologic modelling exercises.

4.5 Future work

Further research should focus on (1) improving the accu-racy of the methodology by better geographical registration methods and coordinated data collection; (2) validating or reformulating the current models using different datasets and

study areas (e.g., other species, mountainous topography) to evaluate parameter stability; (3) exploring the relationships between structural variables obtained from synthetic ALS hemispherical images and satellite-derived spectral indices for watershed- or landscape-level extrapolations; (4) devel-oping alternative methodologies to parameterise hydrologic models with metrics directly obtained from ALS and other remote sensing technologies; and (5) improving the func-tionality of HP processing algorithms to estimate radiation components at sub-daily time steps (e.g., Leach and Moore, 2010). The latter represents a difficult challenge given the inaccuracies in camera orientation, anisotropy of sky bright-ness and atmospheric attenuation, among others; however, if achieved, it would allow the direct input of radiation trans-mission into point-based process simulation of hydrologic models and better performances if above-canopy radiation is available.

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5 Conclusions

To our knowledge, this is the first study that has attempted to re-project discrete ALS individual returns in a polar coordi-nate system to directly model forest structure and radiation regimes with currently available HP image processing tools. Our results suggest that reprojection of the ALS point cloud is necessary if accurate HP-derived estimates of canopy gap fraction, LAI, SVF and solar radiation transmission are re-quired at the point level. The goal of this study was not to provide prediction models with universal application across all forest types and ALS datasets, but to reveal the impor-tance of coordinate transformation for the estimation of GF and other bulk-canopy metrics, and to demonstrate that these variables can be predicted from discrete ALS calibrated with HP. Our main research objective was fulfilled with the current approach as the models developed can operationally predict canopy GF, LAI, SVF and light indices with reasonable ac-curacy in any location within this ALS dataset, regardless of forest type.

When evaluating the strategies to improve hydrologic models with remotely sensed forest structure metrics, two al-ternatives arise: (1) redevelop process equations at the point level based on several years of detailed meteorological data collection to be directly linked with the 3-D capabilities of ALS or TLS to portray canopy structure, and (2) improve the characterisation of forest structure at the landscape level so that spatially explicit versions of the relevant variables can be directly input in existing fully distributed hydrologic models. While the two approaches need to be completed and this can be achieved in parallel, our study focuses on the latter mainly because it has the potential to directly im-prove the modelling of snow and streamflow processes on a larger scale using the current tools available. Here we present the first step towards obtaining fully distributed versions of the forest structure variables needed to parameterise current physically-based hydrologic models. Following the line of approach (2) mentioned above, the next stage consists of cor-relating these metrics – now available at any location within the spatial extent of an ALS dataset – with satellite-derived spectral indices in order to obtain fully distributed structural variables to replace the bulk and discrete vegetation classes that are predominantly used at present. The ultimate goal is to input these detailed, spatially explicit and continuous ver-sions of the variables into fully distributed models to evaluate the changes in model efficiencies when estimating snow ac-cumulation and ablation as well as streamflow generation.

As ALS is becoming increasingly available worldwide, this article represents a major contribution to hydrologic studies by facilitating the estimation of forest structure met-rics relevant to model parameterisation through reduced fieldwork requirements and unlimited, spatially-explicit sam-pling designs.

Acknowledgements. We thank Valerie LeMay and R. Dan Moore

for valuable statistical advice, and Sylvain Leblanc for insights regarding hemispherical photograph processing. This project was funded by a Natural Sciences and Engineering Research Council of Canada (NSERC) PGSD3 scholarship (Andr´es Varhola), and an NSERC Discovery grant (Nicholas Coops). A very special thanks to Jennifer Raguˇz for her prolific and generous proofreading. We greatly appreciate the dedicated work of Wolfgang Wagner (editor), Jenny Lovell, Konrad Schindler and two anonymous referees during the article’s review process.

Edited by: W. Wagner

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Figure

Fig. 1. Study area location within British Columbia (left) includingALS transects (black straight lines in the close-up) and ground plotlocations in the Vanderhoof (top left corner ellipse) and Baker Creek(bottom right corner circle) areas; the 2500 m2 square ground plots(right) are constituted by 36 individual stakes (spaced 10 m) labelledas letter and number combinations (A1 to F6) (Teti, 2008).

Fig 1.

Study area location within British Columbia left includingALS transects black straight lines in the close up and ground plotlocations in the Vanderhoof top left corner ellipse and Baker Creek bottom right corner circle areas the 2500 m2 square ground plots right are constituted by 36 individual stakes spaced 10 m labelledas letter and number combinations A1 to F6 Teti 2008 . View in document p.4
Table 1. Stand locations and physical characteristics as of 2008.

Table 1.

Stand locations and physical characteristics as of 2008 . View in document p.4
Table 2. ALS simple metric summary for each major plot.

Table 2.

ALS simple metric summary for each major plot . View in document p.5
Table 3. Hemispherical photo parameter calibration.

Table 3.

Hemispherical photo parameter calibration . View in document p.6
Table 4. Variable acronyms and description.

Table 4.

Variable acronyms and description . View in document p.7
Fig. 2. Effect of projected ALS return size on the relationship be-tween observed and predicted gap fractions

Fig 2.

Effect of projected ALS return size on the relationship be tween observed and predicted gap fractions. View in document p.8
Fig. 3. Example of the projection of an ALS spherical return intoa 2-D focal plane (a), and azimuthal radial distortion correction atrepresentative zenith angles (b).

Fig 3.

Example of the projection of an ALS spherical return intoa 2 D focal plane a and azimuthal radial distortion correction atrepresentative zenith angles b . View in document p.8
Figure 4 shows examples of ALS return clouds with cor-responding synthetic and actual HP for six common stand5 returns mindividual trees difficult
Figure 4 shows examples of ALS return clouds with cor responding synthetic and actual HP for six common stand5 returns mindividual trees dif cult. View in document p.10
Fig. 5. Relationship between ALS-derived (LGFθ) and HP-derived gap fraction (FGFθ) (a, b, c) and between predicted and observed valuesof gap fraction obtained from simple (d, e, f) and multiple (g, h, i) linear regression models across three representative zenith angle AOV(30◦, top; 60◦, centre; and 90◦, bottom); legends in sub-figures (a) and (i) apply to all.

Fig 5.

Relationship between ALS derived LGF and HP derived gap fraction FGF a b c and between predicted and observed valuesof gap fraction obtained from simple d e f and multiple g h i linear regression models across three representative zenith angle AOV 30 top 60 centre and 90 bottom legends in sub gures a and i apply to all . View in document p.11
Table 5. Correlation matrix showing the coefficient of correlation(r) between variables used in multiple regression (gap fraction only,for simplicity); non-significant (p > 0.05) values shown in italic.

Table 5.

Correlation matrix showing the coef cient of correlation r between variables used in multiple regression gap fraction only for simplicity non signi cant p 0 05 values shown in italic . View in document p.12
Fig. 6. Relationship between gap fraction predicted from multiple linear regression (Eq

Fig 6.

Relationship between gap fraction predicted from multiple linear regression Eq. View in document p.12
Fig. 7. Comparison between the relationship of plot-level averagetion estimated from untransformed ALS, andgap fractions obtained from optical HP and (a) vertical gap frac- (b) gap fractions fromcalibrated synthetic hemispherical images.

Fig 7.

Comparison between the relationship of plot level averagetion estimated from untransformed ALS andgap fractions obtained from optical HP and a vertical gap frac b gap fractions fromcalibrated synthetic hemispherical images . View in document p.13
Table 6. Multiple linear regression results (refer to Table 4 for RMSE and RMSES units).

Table 6.

Multiple linear regression results refer to Table 4 for RMSE and RMSES units . View in document p.14